Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy

Interplay between bending and stretching in carbon nanoribbons

We investigate the bending properties of carbon nanoribbons by combining continuum elasticity theory and tight-binding atomistic simulations. First, we develop a complete analysis of a given bended configuration through continuum mechanics. Then, we provide by tight-binding calculations the value of the bending rigidity in good agreement with recent literature. We discuss the emergence of a stretching field induced by the full atomic-scale relaxation of the nanoribbon architecture. We further prove that such an in-plane strain field can be decomposed into a first contribution due to the actual bending of the sheet and a second one due to edge effects.Comment: 5 pages, 6 figure

Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

Hazard assessment of storm events in the central region of the Portuguese coast

The environmental and socio-economic importance of the coastal areas is widely recognized, but these areas face today severe weaknesses and high-risk situations. The increased demand and human occupation of the coast has greatly contributed to increase such weaknesses. Today, throughout the world, in all countries with coastlines, episodes of waves overtopping and coastal flooding are frequent. These episodes are usually responsible for property losses and often put human lives at risk. The floods are caused by coastal storms due to the action of very strong winds. The propagation of these storms towards the coast induces high water levels. Consequently, carrying out series of storm scenarios and analyzing their impacts through numerical modelling is of prime interest to the coastal decision-makers. A contribution to the preservation and sustainability of the coastal zone constitutes the main aim of this work. Firstly, historical storm tracks and intensities are characterized for the Portuguese coast, in terms of probability of occurrence. Secondly, several storm events with high potential of occurrence are generated using the specific tool DelftDashboard. The hydrodynamic model Delft3D is then used to simulate their effects on currents and on the coastal water levels. Two spatial domains are considered: a large domain encompassing the Iberian coastal zone and a smaller domain for the central region of the Portuguese coast (between cities of Aveiro and Figueira da Foz); this one with a more refined grid. Based on statistical data and by numerical modelling, a review of the impact of coastal storms to different locations within the study area is performed

Variação de procedências para a produção de sementes de Araucaria angustifolia Bert. O. Ktze.

Resumo

Seletividade do óleo de mamona em adultos do Trichogramma pretiosum Riley, 1978 (Hymenoptera: Trichogrammatidae).

Testes de seletividade tornaram-se obrigatórios quando o objetivo é estudar o efeito de um inseticida, mesmo que de origem vegetal, em organismos benéficos. Neste sentido, foi avaliada a seletividade do Óleo de mamona® nas concentrações de 1, 2, 3, 4, 5 e 6% (v/v), do detergente neutro Zupp® a 2% (v/v) (emulsificante para o óleo), do inseticida clorpirifós a 0,5 L i.a./ha (testemunha positiva) e da água destilada em adultos do T. pretiosum, de acordo com protocolos da IOBC/WPRS.Resumo

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu

Viabilidade econômica do sistema agroflorestal grevílea x café na Região Norte do Paraná.

Na década de 70, o Instituto Brasileiro do Café - IBC incentivou a introdução de Grevillea robusta nos cafezais da região Norte do Paraná, na forma de quebra-ventos, apesar de sua implantação não haver seguido padrões técnicos adequados. Para a análise da viabilidade econômica da utilização desses quebra-ventos, foram comparados os benefícios diretos (custos x renda) do Sistema Puro Café e do Sistema Agroflorestal Grevílea x Café, utilizando um aplicativo de apropriação e análise de custos, o SAAC florestal (Hildebrandt, 1995). As planilhas do aplicativo foram preenchidas separadamente para os dois sistemas. O Sistema Puro Café contou com dados secundários de custos de produção e rendas fornecidos por órgãos públicos e privados. Para a análise do Sistema Agroflorestal, foram utilizados os mesmos dados referentes à produção monocultural de café, acrescidos dos dados de custos de produção e rendas da espécie florestal obtidos por meio de questionários aplicados junto a proprietários rurais e serrarias da região de estudo. Os resultados obtidos permitiram constatar que a espécie florestal introduzida no sistema representa um custo adicional insignificante para o produtor rural e ocupa uma área mínima, ou seja, uma média de 58 árvores por hectare. A renda obtida com a venda da madeira para serrarias gera um aumento significativo da renda no último ano, de 32,22%, permitindo o pagamento dos custos de implantação ou grande parte dos custos de reforma da atividade. Portanto, a utilização da grevílea nos cafezais é altamente positiva do ponto de vista do aumento da rentabilidade da atividade e da tranquilidade do produtor, pois pode representar uma poupança ao longo do ciclo da cultura cafeeira, assegurando a continuidade desta atividade por meio do pagamento da reforma com o corte da madeira

Contribution to the preservation of healthy coastal ecosystems

The release of pollutants into coastal zones from municipal and/or industrial drainage systems is a problem with a considerable environmental impact. In order to minimize the contamination of coastal waters in certain places (e.g., along beaches and in aquacultures), solutions based on the construction of submarine sewer outfalls have been proposed. In order to ascertain the optimal conditions for the release of an emissary, in particular the place of release, it is necessary to characterize the hydrodynamic transport processes that govern the evolution and mixture of pollutants in the area of interest. Circulation in the coastal zone is complicated, given that it is determined by a set of forcing mechanisms of diverse origins (meteorological, astronomical, large-scale ocean circulation, etc.) that endow it with a considerable space-time variation. Wastewater plume behaviour and characteristics depend both on the receiving water conditions and on the discharge characteristics. Accordingly, the implementation of a submarine outfall system requires a prior study of the site where the outfall is to be constructed, in order to achieve optimal rates of dilution of the pollutants released to the environment. Mathematical modelling appears to be a very useful tool for coastal zone environmental management either for continuous monitoring analysis or in accidental ecosystem rupture. This work presents some results and conclusions of two case studies. The first is a study of the pollutant cloud released at the São Jacinto submarine sewer outfall, located about 3 km offshore and 3 km north of an important coastal lagoon (NW Portugal). The main focus of this study was to establish the hydrodynamic conditions in which the pollutant release might affect the coastline (principally the existing beaches and lagoon). The second case presents some hydrodynamic results and water quality aspects of the Ria de Arosa (NW Spain), and also includes an assessment of the environmental impact of wastewater discharges from nine submarine outfalls considered in the sanitation plan of this bay. Results of faecal matter concentration distribution were used in the discussion on the outfall discharges’ impact on the natural water system for different hydrodynamic scenarios. In both cases, 3D numerical models were used